“The Life-Spans of Empires”, Samuel Arbesman2011-07-28 (; backlinks; similar)⁠:

Figure 1: Lifetime distribution of empires. The best-fit line for the exponential distribution is overlaid on the lifetime distribution of 41 empires. The bin height is the frequency of empires in each bin, divided by the bin width, to arrive at a probability density.

The collapse of empires is exceedingly difficult to understand.

The author examined the distribution of imperial lifetimes using a data set that spans more than 3 millennia and found that it conforms to a memoryless exponential distribution in which the rate of collapse of an empire is independent of its age.

Comparing this distribution to similar lifetime distributions of other complex systems—specifically, biological species and corporate firms—the author explores the reasons behind their lifetime distributions and how this approach can yield insights into empires.

[Keywords: empires, exponential lifetime, longevity, species]